We present a chemical abundance study of the brightest confirmed member star of the ultra-faint dwarf galaxy Boötes II from Keck/HIRES high-resolution spectroscopy at moderate signal-to-noise ratios. At [Fe/H] = –2.93 ± 0.03(stat.) ± 0.17(sys.), this star chemically resembles metal-poor halo field stars and the signatures of other faint dwarf spheroidal galaxies at the same metallicities in that it shows enhanced [α/Fe] ratios, Solar Fe-peak element abundances, and low upper limits on the neutron-capture element Ba. Moreover, this star shows no chemical peculiarities in any of the eight elements we were able to measure. This implies that the chemical outliers found in other systems remain outliers pertaining to the unusual enrichment histories of the respective environments, while Boo II appears to have experienced an enrichment history typical of its very low mass. We also re-calibrated previous measurements of the galaxy's metallicity from the calcium triplet (CaT) and find a much lower value than reported before. The resulting broad metallicity spread, in excess of one dex, the very metal-poor mean, and the chemical abundance patterns of the present star imply that Boötes II is a low-mass, old, metal-poor dwarf galaxy and not an overdensity associated with the Sagittarius Stream as has been previously suggested based on its sky position and kinematics. The low, mean CaT metallicity of –2.7 dex falls right on the luminosity-metallicity relation delineated over four orders of magnitude from the more luminous to the faintest galaxies. Thus Boötes II's chemical enrichment appears representative of the galaxy's original mass, while tidal stripping and other mass loss mechanisms were probably not significant as for other low-mass satellites.